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We develop a theoretical framework for generalization in the interpolating regime of statistical learning. The central question is why highly overparameterized estimators can attain zero empirical risk while still achieving nontrivial predictive accuracy, and how to characterize the boundary between benign and destructive overfitting. We introduce a spectral-transport stability framework in which excess risk is controlled jointly by the spectral geometry of the data distribution, the sensitivity of the learning rule under single-sample replacement, and the alignment structure of label noise. This leads to a scale-dependent Fredriksson index that combines effective dimension, transport stability, and noise alignment into a single complexity parameter for interpolating estimators. We prove finite-sample risk bounds, establish a sharp benign-overfitting criterion through the vanishing of the index along admissible spectral scales, and derive explicit phase-transition rates under polynomial spectral decay. For a model-specific specialization, we obtain an explicit theorem for polynomial-spectrum linear interpolation, together with a proof of the resulting rate. The framework also clarifies implicit regularization by showing how optimization dynamics can select interpolating solutions of minimal spectral-transport energy. These results connect algorithmic stability, double descent, benign overfitting, operator-theoretic learning theory, and implicit bias within a unified structural account of modern interpolation.

For example, hats and sunglasses are placed on incorrect objects. We introduce a novel method T oMeto address these challenges.

TPT does not explicitly align the pre-trained CLIP to become aware of the test sample distribution. For the effective test-time adaptation of V -L foundation models, it is crucial to bridge the distribution gap between the pre-training dataset and the downstream evaluation set for high zero-shot generalization.

Scene flow estimation is an essential ingredient for a variety of real-world applications, especially for autonomous agents, such as self-driving cars and robots.

Then, we present the error bar plots with mean D-ECE and std deviation (Sec. The error in particular detection is computed as it satisfies the false positive criteria. We report D-ECE on these challenging out-domain scenarios. (Figure 1). We show the bar plots depicting mean D-ECE with respective standard deviations.

Left: The reward function is a mixture of Gaussian, and the offline data distribution is unbalanced with most samples located in low-reward states.